Multiply the following complex numbers: $({3}) \cdot ({5-5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3}) \cdot ({5-5i}) = $ $ ({3} \cdot {5}) + ({3} \cdot {-5}i) + ({0}i \cdot {5}) + ({0}i \cdot {-5}i) $ Then simplify the terms: $ (15) + (-15i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 15 + (-15 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 15 + (-15 + 0)i - 0 $ The result is simplified: $ (15 - 0) + (-15i) = 15-15i $